FarZone4IT: A MatLab-based software for the calculation of far-zone effects for spherical integral transformations

Abstract

Integral transformations are a useful mathematical apparatus for modelling the gravitational field. They represent the mathematical basis for formulating integral estimators of gravitational field values, including error propagation. The theoretical and practical aspects of integral transformations traditionally used for calculating geoid/quasigeoid heights in geodesy, such as Stokes’s and Hotine’s integral transformations, have already been studied. However, theoretical and practical concepts regarding other integral transformations, including non-isotropic (azimuth-dependent) transformations, have yet to be explored. One of the basic assumptions of integral transformations is global data coverage. However, the availability of ground measurements is frequently limited. In practice, the global integral is divided into two complementary regions: the near- and far–zones. Non–negligible systematic effects of data in the far-zone require accurate evaluation. For this purpose, a new software library is developed in the MatLab environment to calculate far–zone effects for integral transformations for gravitational potential gradients up to the third order. The library contains scripts for calculating integral kernels, error kernels, truncation error coefficients, and far-zone effects for a selected set of input parameters. This contribution deals with implementing equations defining far-zone effects and the subsequent numerical testing of the library functionality. Closed-loop tests were carried out using gravitational potential functionals generated from a global Earth’s gravitational field model to check the numerical correctness of the software library.